Emergence of a non-scaling degree distribution in bipartite networks: A numerical and analytical study

¹  Max Planck Institute for the Physics of Complex Systems - Nöthnitzer Strasse 38, 01187 Dresden, Germany
²  ZIH, Technische Universität Dresden - Zellescher Weg 12, 01069 Dresden, Germany
³  Department of Computer Science and Engineering, Indian Institute of Technology - Kharagur, India

Received: 25 March 2007
Accepted: 4 June 2007

Abstract

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We derive the exact analytical expression for the degree-distribution of all these different types of attachments while assuming that edges are incorporated sequentially, i.e., a single edge is added to the growing network in a time step. We also provide an approximate expression for the case when more than one edges are added in a time step. We show that depending on the relative weight between random and preferential attachments, the degree-distribution of this type of network falls into one of the four possible regimes, which range from a binomial distribution for pure random attachment to an u-shaped distribution for dominant preferential attachment.